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IGCSE Physics

Waves

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Lesson 7 – RefractionAims:

•To describe experiments to investigate the refraction of light, using rectangular blocks, semicircular blocks and triangular prisms.

•To recall and use the relationship between refractive index, angle of incidence and angle of refraction n = (sin i) / (sin r).

•To describe an experiment to determine the refractive index of glass, using a glass block.

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Introducing refraction

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Refraction of light

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The rays of light from a stone get bent (refracted) as they leave the water.

Your brain assumes these rays of light have travelled in straight lines.

Your brain forms an image at the place where it thinks the rays have come from – the stone appears to be higher than it really is.

actual location

image

Real and apparent depth

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image of prey

prey location

The fish does not aim at the refracted image it sees but at a location where it knows the prey to be.

The Archer fish allows for the refraction of light at the surface of the water when aiming at the prey.

The Archer fish

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Refraction diagrams and law of refraction

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What do you notice about the light rays either side of the glass block?

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airglass

When light is refracted as it travels from air to glass:angle of incidence > angle of refraction

i > r

In general, when light rays move from a less dense medium (air) to a more dense medium (glass) they ‘bend’ towards the normal.

As the light ray travels from air into glass it moves towards the normal.

i > r

Air to glass

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air

glass

If the two surfaces of the block are parallel, then the ray at the start is parallel to the ray at the end.

When light is refracted as it travels from air to glass:angle of incidence < angle of refraction

i < r

In general, when light rays travel from a more dense medium (glass) to a less dense medium (air) they ‘bend’ away from the normal.

As the light ray travels from glass into air it moves away from the normal.

i < r

Glass to air

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airglass

What happens to light travelling from air through a glass block when the angle of incidence is 0°?

i = 0°

When the angle of incidence is 0 the light ray is not deviated from its path.

undeviated light ray

Refraction – angle of incidence

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Refraction of light

Conclusion

When light enters glass or water it bends towards the normal line. When light leaves glass or water it bends away from the normal line.

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When waves in water travel through water of different depths they change speed. In shallow water the waves slow down; in deeper water they speed up.

We can investigate this by changing the depth of the water in a ripple tank.

Perspex sheet used to change depth of water

As the water waves slow down, their direction changes due to the change of speed. This is called refraction.

Refraction in water waves

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mud

road

Imagine a car driving from the road into a muddy field.

In the muddy field it slows down as there is more friction.

If it enters the field at an angle then the front tyres hit the mud at different times.

Tyre 1 hits the mud first and will move more slowly than tyre 2. This causes the car to turn towards the normal.

When the car leaves the mud for the road, tyre 1 hits the road before tyre 2 and this causes the car to turn away from the normal.

tyre 1 tyre 2

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If the car approached the muddy field at an angle of incidence of 0° then both front tyres would hit the mud at the same time.

The tyres would have the same speed relative to each other so the direction of the car would not change, it would just slow down.

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Formula and examples

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In the water.

Light moves slower through a more dense medium.

If you were running along a beach and then ran into the water when would you be moving slower – in the water or on the sand?

Do you think light moves faster or slower in a more dense medium?

In a similar way, as light moves from one medium to another of different density, the speed of light changes.

Travelling through different materials

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glass

air

The speed of light waves depends on the material they are travelling through.

air = fastest diamond = slowestglass = slower

If light waves enter a different material (e.g. travelling from glass into air) the speed changes.

This causes the light to bend or refract.

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Speed oflight(thousandskm/s)

From this bar chart, which material do you think is denser, glass or water?

Glass must be denser than water because light travels more slowly through glass than water.

Light travels at 300,000 km/s in a vacuum.

As light enters denser media, the speed of light decreases.

The speed of light

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Glass and water

Glass is denser than water. Light travelling through glass will be refracted more than light travelling through water.

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We can study refraction of light by comparing its speed in air to that in a different material.

A number called the refractive index is the ratio of these two speeds:

Example:

The speed of light in air is 300,000,000 m/s, and the speed of light in water is 225,000,000 m/s. What is the refractive index of water? 1.33

Refractive index = speed of light in air speed of air in material

The speed of light

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The speed of light in air is 300,000,000 m/s.

The speed of light in crystal is 150,000,000 m/s. What is the refractive index of crystal?

Refractive index = speed of light in airspeed of light in crystal

Refractive index = 300,000,000 150,000,000

Refractive index of crystal = 2.0

Calculating refractive index

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Snell’s lawSnell’s law can be used in experiments and calculations to find out the refractive index of a material.

Refractive index = sin i sin r

n = Refractive Index,

i = Angle of incidence,

r = Angle of refraction.

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Snell’s law – Example 1

A light ray incident upon a glass block at 45º is refracted to 28º, calculate the refractive index of the glass.

n = sin i sin r

n = sin (45) sin (28)

n = 0.71 0.47

n = 1.51

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Snell’s law – Example 2

A light ray incident upon a glass block at 48º is refracted to 32º, calculate the refractive index of the glass.

n = sin i sin r

n = sin (48) sin (32)

n = 0.74 0.53

n = 1.40

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Snell’s law – Example 3

A light ray incident upon a glass block is refracted to 25º by a block of refractive index 1.55, calculate the angle of incidence.

n = sin i sin r

sin i = n × sin r

sin i = 1.55 × sin (25)

sin i = 1.55 × 0.42 = 0.66

i = 41º

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Snell’s law – Example 4

A light ray is incident at 60º to a material with refractive index of 2.4 Calculate the angle of refraction of the light ray.

n = sin i sin r

sin r = sin i n

sin r = sin (60) 2.4

sin r = 0.87 2.4 = 0.36

r = 21º

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Experiment

You need to know this experiment for your IGCSE examination

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Determining refractive index

Aim:

• To determine the refractive index of a perspex block.

Method:

• Use a slit and raybox to illuminate a glass block at a range of angles.

• Carefully record the angle of incidence and angle of refraction each time.

• Complete the following table:

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Refractive index table

Angle of incidence

Sin (i) Angle of refraction

Sin (r)

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Graph and gradient

•Draw a graph of sin (i) against sin (r).

•Calculate the gradient of the graph.

•The refractive index of the glass is equal to the gradient of the graph.

Remember

n = sin (i) sin (r)

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Animated refraction

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Summary – Refraction •When light changes the material it is travelling through it is refracted. The change in material causes a change in speed.

•Light entering a glass block from air is refracted towards the normal line and light leaving glass is refracted away from the normal line.

•Snell’s law is given by

n = sin i sin r

•Where: n = refractive index, i = angle of incidence in the air and r = angle of refraction in the medium.